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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 5
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Original Articles

Interaction of radiation with double-diffusive natural convection in a three-dimensional cubic cavity filled with a non-gray gas mixture in cooperating cases

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Pages 479-496 | Received 13 Mar 2015, Accepted 18 Jul 2015, Published online: 30 Nov 2015
 

ABSTRACT

A three-dimensional (3D) numerical study has been performed to investigate the effects of non-gray gas radiation on double-diffusive natural convection in a cubic enclosure filled with either air–H2O or air–CO2 mixtures in cooperating situations. Gas radiation was taken into account by the discrete ordinates method (DOM) associated with the spectral line weighted-sum-of-gray-gases (SLW) spectral model. Results obtained for two average concentrations of H2O and CO2 (10% and 20%) show that radiation modifies the temperature and concentration structures by creating oblique stratifications. The heat transfer rate is decreased, whereas mass transfer is not much modified. In addition, a comparison between 2D and 3D results is presented.

Nomenclature

a=

weighting coefficient in the SLW model

C=

species concentration, mol/m3

Cabs=

absorption cross-section m2/mol

cp=

mixture specific heat capacity, J/kg · K

D=

binary mass diffusion coefficient, m2/s

g=

gravitational acceleration, m/s2

I=

radiation intensity, W/m2 · sr

L=

enclosure length, m

Le=

Lewis number

M=

number of discrete directions

N=

buoyancy ratio

Ng=

number of gray gas

Nu=

Nusselt number

P=

total pressure, Pa

qinc=

incident heat flux at wall, W/m2

qR=

radiative flux, W/m2

Ra=

thermal Rayleigh number [ = g βT(TH − TCL3/(να)]

rw=

given position on the wall

s=

direction of radiation propagation

S=

dimensionless concentration

Sh=

Sherwood number

T=

temperature, K

u, v, w=

velocity components, m/s

U, V, W=

dimensionless velocity components

x, y, z=

space coordinates, m

X, Y, Z=

dimensionless space coordinates

xCO2=

average molar fraction of CO2 at reference conditions

xH2O=

average molar fraction of H2O at reference conditions

α=

mixture thermal diffusivity, m2/s

βC=

mass expansion coefficient, m3/mol

βT=

thermal expansion coefficient, 1/K

ε=

emissivity of the wall

κ=

absorption coefficient, 1/m

λ=

mixture thermal conductivity, W/m × K

θ=

dimensionless temperature

μ,η, ζ=

direction cosines

ν=

mixture kinematic viscosity, m2/s

ρ=

mixture density, kg/m3

σ=

Stefan–Boltzmann constant, W/m2 × K4

w=

weight of angular quadrature

Subscript=
b=

black body

c=

convective or cold

H=

high

h=

hot

i, j, k=

coordinate indices

L=

low

l=

lth gray gas

r=

radiative quantity

t=

total quantity

0=

reference value

w=

wall

Nomenclature

a=

weighting coefficient in the SLW model

C=

species concentration, mol/m3

Cabs=

absorption cross-section m2/mol

cp=

mixture specific heat capacity, J/kg · K

D=

binary mass diffusion coefficient, m2/s

g=

gravitational acceleration, m/s2

I=

radiation intensity, W/m2 · sr

L=

enclosure length, m

Le=

Lewis number

M=

number of discrete directions

N=

buoyancy ratio

Ng=

number of gray gas

Nu=

Nusselt number

P=

total pressure, Pa

qinc=

incident heat flux at wall, W/m2

qR=

radiative flux, W/m2

Ra=

thermal Rayleigh number [ = g βT(TH − TCL3/(να)]

rw=

given position on the wall

s=

direction of radiation propagation

S=

dimensionless concentration

Sh=

Sherwood number

T=

temperature, K

u, v, w=

velocity components, m/s

U, V, W=

dimensionless velocity components

x, y, z=

space coordinates, m

X, Y, Z=

dimensionless space coordinates

xCO2=

average molar fraction of CO2 at reference conditions

xH2O=

average molar fraction of H2O at reference conditions

α=

mixture thermal diffusivity, m2/s

βC=

mass expansion coefficient, m3/mol

βT=

thermal expansion coefficient, 1/K

ε=

emissivity of the wall

κ=

absorption coefficient, 1/m

λ=

mixture thermal conductivity, W/m × K

θ=

dimensionless temperature

μ,η, ζ=

direction cosines

ν=

mixture kinematic viscosity, m2/s

ρ=

mixture density, kg/m3

σ=

Stefan–Boltzmann constant, W/m2 × K4

w=

weight of angular quadrature

Subscript=
b=

black body

c=

convective or cold

H=

high

h=

hot

i, j, k=

coordinate indices

L=

low

l=

lth gray gas

r=

radiative quantity

t=

total quantity

0=

reference value

w=

wall

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